Information Loss in Generalized Symmetry Breaking

arXiv:2509.24625 · quant-ph, hep-th, math-ph, math.MP · Submitted 2025-09-29 · Read on arXiv

quant-ph, hep-th, math-ph, math.MP

Submitted: 2025-09-29

Updated: 2026-09-17

Comments: v4: 31 pages, SciPost Submission. Revised version according to referee comments and reports. Results and conclusions unchanged. Improved presentation and additional discussion of the examples. References added

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Anyon Condensation — 22× in this paper · explained in 1 episode
• Symmetry Breaking — 11× in this paper · explained in 3 episodes
• Trace — 10× in this paper · explained in 2 episodes
• Anyons — 7× in this paper · explained in 2 episodes
• Consistency — 6× in this paper · explained in 3 episodes
• Topological Order — 6× in this paper · explained in 2 episodes
• Phase Transitions — 4× in this paper · explained in 2 episodes
• Information-Theoretic Framework — 3× in this paper · explained in 2 episodes
• Adjacency Matrix — 2× in this paper · explained in 1 episode
• Entanglement — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Topological Defects — 1× in this paper · explained in 2 episodes
• alpha — 1× in this paper · explained in 1 episode

Sources

• Generalized Global Symmetries
• Generalized Symmetries in Condensed Matter
• Categorical Landau Paradigm for Gapped Phases
• Non-invertible symmetries and selection rules for RG flows of coset models
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• Gauging Non-Invertible Symmetries: Topological Interfaces and Generalized Orbifold Groupoid in 2d QFT
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Phases with non-invertible symmetries in 1+1D $\unicode{x2013}$ symmetry protected topological orders as duality automorphisms
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part II
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Classification of 1+1D gapless symmetry protected phases via topological holography
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Gapless Phases in (2+1)d with Non-Invertible Symmetries
• Topological Holography for 2+1-D Gapped and Gapless Phases with Generalized Symmetries
• Entropic order parameters for the phases of QFT
• Lectures on entanglement in quantum field theory

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